Strand: Processing: Students must be able to reason, solve problems, and communicate their understanding in effective ways. The problems the students are expected to solve and their use of mathematical language becomes more complex and sophisticated as the student progresses through the mathematics curriculum. These increased expectations are reflected in the increase complexity of the content and rigor as the students deal with more challenging problems.
Concept 1: Problem-Solving
Benchmark: Apply and adapt a variety of appropriate strategies and resources to solve a problem
Benchmark: Identify relevant, extraneous, and missing information related to the solution of a problem
Benchmark: Attempt to solve all problems (not sure about this one—measurable?)
Benchmark: Monitor and reflect on the process used to solve a problem
Benchmark: Build new mathematical knowledge using previous mathematical knowledge
Benchmark: Solve problems that arise in other contexts (more specific? How is this measured/assessed?)
Concept 2: Communication
Benchmark: Organize and consolidate mathematical thinking
Benchmark: Communicate mathematical thinking coherently and clearly
Benchmark: Analyze and evaluate mathematical thinking of others
Benchmark: Use the language of mathematics to express mathematical ideas
JAK: I think these are good and relatively clear. Under problem solving, I commented on two benchmarks parenthetically; I am not sure the first of those two benchmarks is something for the standards, the second might just be rephrase (what does other contexts mean? Are we trying to say applying mathematical problem solving outside of the mathematics classroom?). Could benchmark 2 and benchmark 4 under Communication be combined? Just a reminder that the benchmarks should express ideas, skills, content, etc that is measurable by some sort of assessment, so we’ll want to keep that in mind as we think about how these benchmarks are articulated. One observation is that the first sentence of the “Processing” description includes, problem solving, communication, and reasoning, but we don’t have a Concept for reasoning. That’s okay with me if you want it that way, but just something to think about.
Grade: 6-12
Strand: Processing: Students must be able to reason, solve problems, and communicate their understanding in effective ways. The problems the students are expected to solve and their use of mathematical language becomes more complex and sophisticated as the student progresses through the mathematics curriculum. These increased expectations are reflected in the increase complexity of the content and rigor as the students deal with more challenging problems.
Concept 1: Problem-Solving
Concept 2: Communication
JAK: I think these are good and relatively clear. Under problem solving, I commented on two benchmarks parenthetically; I am not sure the first of those two benchmarks is something for the standards, the second might just be rephrase (what does other contexts mean? Are we trying to say applying mathematical problem solving outside of the mathematics classroom?). Could benchmark 2 and benchmark 4 under Communication be combined? Just a reminder that the benchmarks should express ideas, skills, content, etc that is measurable by some sort of assessment, so we’ll want to keep that in mind as we think about how these benchmarks are articulated. One observation is that the first sentence of the “Processing” description includes, problem solving, communication, and reasoning, but we don’t have a Concept for reasoning. That’s okay with me if you want it that way, but just something to think about.